Solve Using the Quadratic Formula 3x^2-7x-6=0

Problem

3*x2−7*x−6=0

Solution

1. Identify the coefficients of the quadratic equation in the form a*x2+b*x+c=0

a=3

b=−7

c=−6

2. State the quadratic formula used to find the solutions for x

x=(−b±√(,b2−4*a*c))/(2*a)

3. Substitute the values of a b and c into the formula.

x=(−(−7)±√(,(−7)2−4*(3)*(−6)))/(2*(3))

4. Simplify the expression inside the square root (the discriminant).

x=(7±√(,49+72))/6

x=(7±√(,121))/6

5. Evaluate the square root of the discriminant.

x=(7±11)/6

6. Solve for both possible values of x by calculating the addition and subtraction cases separately.

x=(7+11)/6=18/6=3

x=(7−11)/6=(−4)/6=−2/3

Final Answer

x=3,−2/3

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